Sensing and Control of Dynamical Systems Over Networks

Abstract: Rapid advances in sensing, computing, and wireless technologies have led to significant interest in the understanding and development of wireless networked control systems. Networked control systems consist of spatially distributed agents such as plants (dynamical systems), sensors, and controllers, that interact to achieve desired objectives. The sensors monitor the plants and communicate measurements to remotely situated controllers. The controllers apply actions to stabilize and control the plants.  Such systems have diverse applications in security, surveillance, industrial production, health monitoring, remote surgery, environment management, space missions, and intelligent transport systems. The objective of the thesis is to understand the fundamental limits and principles involved in the design of sensing and control strategies for dynamical systems controlled over communication networks.The thesis has three parts. Part I and Part III consider the design of sensing and control strategies for mean-square stabilization of linear dynamical systems over fundamental communication channels such as point-to-point, relay, multiple-access, broadcast, and interference channels. The sensors and other nodes within the communication network are assumed to have average power transmit constraints. Moreover, the communication links between all agents (plants, sensors, controllers) are modeled as Gaussian channels. Necessary as well as sufficient conditions for mean-square stabilization over various network topologies are derived. The necessary conditions are arrived at using information theoretic arguments such as properties of mutual information, directed information, and differential entropy. The sufficient conditions are obtained using delay-free sensing and control policies. These conditions quantify the effect of communication network parameters such as transmit powers, channel noise, and channel interference on the stability of the plant(s). Different settings where linear policies are optimal, asymptotically optimal (in certain parameters of the system) and suboptimal have also been identified. Part II considers the design of real-time sensing and control strategies for minimization of a quadratic cost function of the state process of a system over Gaussian networks. Two fundamental Gaussian networks are considered: i) cascade network and ii) parallel network. For each network, non-linear sensing and control schemes are proposed and sub-optimality of linear strategies is discussed.The results reveal fundamental limits on the performance of linear systems controlled over Gaussian networks. The methods used to derive these results reveal a close interplay between information theory and control theory.